On the $p$ -Schur property of Banach spaces

Dehghani, Mohammad B.; Moshtaghioun, Seyed Mohammad

doi:10.1215/20088752-2017-0033

Cited by 18 publications

(24 citation statements)

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“…Since X has the p-(RDP P ) p , T ∈ C p (X, Y ) ∩ W p (X, Y ). Thus, an application of Corollary 2.23 in [6] shows that, T is strictly singular. Corollary 2.8.…”

Section: Resultsmentioning

confidence: 91%

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

Alikhani

2019

Adv. Oper. Theory

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In this article, we study the relationship between p-(V ) subsets and p-(V * ) subsets of dual spaces. We investigate the Banach space X with the property that adjoint every p-convergent operator T : X → Y is weakly q-compact, for every Banach space Y. Moreover, we define the notion of qreciprocal Dunford-Pettis * property of order p on Banach spaces and obtain a characterization of Banach spaces with this property. Also, the stability of reciprocal Dunford-Pettis property of order p for projective tensor product is given.2010 Mathematics Subject Classification. Primary 46B20; Secondary 46B25, 46B28. Key words and phrases. p-convergent operators, reciprocal Dunford-Pettis property and Dunford-Pettis property of order p..

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“…Since X has the p-(RDP P ) p , T ∈ C p (X, Y ) ∩ W p (X, Y ). Thus, an application of Corollary 2.23 in [6] shows that, T is strictly singular. Corollary 2.8.…”

Section: Resultsmentioning

confidence: 91%

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

Alikhani

2019

Adv. Oper. Theory

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“…(ii) ⇒ (i) By our hypothesis, X * contains no isomorphic copy of c 0 . Therefore Theorem 2.4 in [10] implies that X * has the 1-Schur property and so X * has the 1-(DPrcP). Therefore, by Lemma 3.4(iii), B X is a 1-Right * set in X.…”

Section: (P Q)-sequentially Right Property On Banach Spacesmentioning

confidence: 94%

“…(i) ⇒ (ii) is obvious. (ii) ⇒ (i) Since X contains no isomorphic copy of c 0 , X has the 1-Schur property; (see Theorem 2.4 in [10]) and so has the 1-(DPrcP). Hence, B X * is a 1-Right subset of X * .…”

Section: (P Q)-sequentially Right Property On Banach Spacesmentioning

confidence: 98%

Sequentially right-like properties on Banach spaces

Alikhani

2019

Filomat

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In this paper, we study first the concept of p-sequentially Right property, which is p-version of the sequentially Right property. Also, we introduce a new class of subsets of Banach spaces which is called p-Right * set and obtain the relationship between p-Right subsets and p-Right * subsets of dual spaces. Furthermore, for 1 ≤ p < q ≤ ∞, we introduce the concepts of properties (SR) p,q and (SR *) p,q in order to find a condition such that every Dunford-Pettis q-convergent operator is Dunford-Pettis p-convergent. Finally, we apply these concepts and obtain some characterizations of the p-Dunford-Pettis relatively compact property of Banach spaces and their dual spaces.

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“…We denote the space of all p-convergent operators from X into Y, by C p (X, Y ); see [6]. If the identity operator on X is p-convergent, we say that a Banach space X has the p-Schur property, which is equivalent to every weakly p-compact subset of X is norm compact; see [12]. A Banach space X is said to have the Dunford-Pettis property of p (in short, (DP P p )), if for any Banach space Y, every weakly compact operator T :…”

Section: Notions and Definitionsmentioning

confidence: 99%

Some applications of uniformly $ p $-convergent sets

Alikhani

2020

Preprint

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In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact sets. Moreover, we introduce the concept of weakly p-sequentially continuous differentiable mappings and obtain some characterizations of these mappings. Finally, we give a factorization result for differentiable mappings through p-convergent operators.

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On the $p$ -Schur property of Banach spaces

Cited by 18 publications

References 0 publications

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

Sequentially right-like properties on Banach spaces

Some applications of uniformly $ p $-convergent sets

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